Finite Volume Analysis of Relativistic Field Theories Using Lattice Regularization

使用格正则化的相对论场论的有限体积分析

基本信息

批准号：
1913010
负责人：
Rajamani Narayanan
金额：
$ 24.03万
依托单位：
Florida International University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-07-15 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1913010&HistoricalAwards=false
关键词：
Finite Volume Analysis Relativistic Field

项目摘要

Quantum Chromo Dynamics (QCD) is a theory that describes one of the fundamental interactions in nature, namely, strong interactions. The fundamental degrees of freedom are quarks (particles) and gluons (force mediators). Gauge fields (gluons) coupled to massless fermions (quarks) have no free parameters and they have no intrinsic scale. Depending on the nature of the gauge group and the fermionic content, these theories fall into two categories upon quantization: One that maintains scale invariance and contains only massless excitations and one that breaks scale invariance and produces a rich spectrum of massive excitations. Whether the quantum theory is scale invariant or not, it is always strongly interacting and a non-perturbative formalism is necessary to study why some theories are scale invariant and the others are not. It is also necessary to study the flow from one theory to another and try to understand how a scale emerges. The PI will extract properties of theories in both classes (scale invariant and scale breaking) and study the flow of a scale invariant theory to a theory that breaks scale invariance. This will enable us to understand the emergence of the fundamental scale in strong interactions.Lattice formalism of gauge fields coupled to massless fermions is a well tested approach to the extraction of the fundamental non-perturbative properties of these theories. Theories that break scale invariance have been studied in great detail using this method. The PI will use the lattice formalism and study potentially scale invariant theories in a finite periodic box. The size of the box sets an external scale and the PI will be able to extract the scale invariant properties of a theory by studying the asymptotic behavior as a function of the external scale. By fixing the gauge group and varying the number of fermion flavors by one unit around a critical number of fermion flavors the PI will start with one theory (larger number of fermion flavors) and add a mass term for one of the fermion flavors. By varying the mass parameter from zero to infinity, the PI will be able to flow between two theories where both of them are scale invariant at the classical level but one (fewer number of fermion flavors) breaks the scale invariance at the quantum level.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

量子Chromo动力学（QCD）是一种描述自然界中基本相互作用之一的理论，即强烈的相互作用。自由的基本程度是夸克（颗粒）和胶子（力介体）。耦合到无质量费米子（夸克）的量规场（胶子）没有自由参数，并且没有内在的尺度。根据量规组的性质和费米子含量，这些理论在量化后分为两类：一种保持规模的不变性，并且仅包含无质量激发，一种可以破坏规模的不变性并产生丰富的大量激励。无论量子理论是否是规模不变的，它始终是强烈的相互作用，而非扰动形式主义是研究为什么某些理论是规模不变而其他理论却不是必要的。还必须研究从一种理论到另一种理论的流程，并尝试了解量表的出现。 PI将在两个类别（规模不变和规模破裂）中提取理论的特性，并研究量表不变理论的流动到破坏规模不变性的理论。这将使我们能够理解强烈相互作用中基本量表的出现。量规范的局部形式与无质量费米子耦合是一种经过良好测试的方法，用于提取这些理论的基本非扰动特性。使用此方法对破坏规模不变性的理论进行了详细的研究。 PI将使用晶格形式主义，并在有限的周期盒中研究潜在的规模不变理论。盒子的大小设定了外部尺度，PI将能够通过研究渐近行为作为外部尺度的函数来提取理论的规模不变特性。通过固定量规组并将费米的数量通过一个单元在临界数量的Fermion风味周围变化，PI将以一种理论（较大数量的费米风味）开始，并为其中一种费米昂的口味添加质量项。通过将质量参数从零变为无穷大，PI将能够在两种理论之间流动，在这两种理论中，它们在经典级别上都是规模不变的，但一个（较少数量的费米昂风味）破坏了量子的规模不变性，在量子级别上的规模不变性。该奖项反映了NSF的法定任务，并通过评估范围来反映了众所周知的范围。